The Kiwis held off a late fightback from Australia to claim the trophy at Wellington's Westpac Stadium on Saturday, with Johnson scoring a try and serving as New Zealand's main attacking architect in a fine individual performance.
Victory for Stephen Kearney's men marked the first time in over 60 years that New Zealand had claimed back-to-back wins over Australia, having beaten them in the opening game of the tournament last month.
And half-back Johnson was quick to express his delight after his inspirational showing helped New Zealand recapture the title they last won in 2010.
"We'd waited quite a while for this and I'm just so proud of the boys. It's a dream come true," Johnson said.
"We worked so hard this tour. It's been such an awesome tournament for the boys and to finish it off like that has just been unreal.
"I feel that [Kearney] has just given me a lot of confidence just to have a crack and our forwards have been unreal this whole tournament.
"They laid the platform and it's been us on the back of it. I like running and I was able to do that tonight."
Meanwhile, Australia captain Cameron Smith conceded his side did not deserve to emerge victorious.
"Congratulations to the Kiwi boys on a fantastic tournament," Smith said. "You've gone through undefeated and that's a pretty special effort.
"It's been a bit of an up-and-down tournament for us. We didn't start too well but I thought in the last couple of weeks we played some good footie. Tonight we were pretty brave but unfortunately we came up against a better side."